convert.py

from math import log


def is_valid_number(number, base):
    for i in reversed(range(int(log(number, 10)) + 1)):
        digit = number / 10 ** i
        number -= digit * 10 ** i

        if digit >= base:
            return False

    return True


def convert(number, source_base=10, target_base=10, validate=True):
    if number == 0:
        return number

    if validate:
        if source_base < 2 or source_base > 10:
            raise ValueError("Invalid base: %s" % source_base)
        if target_base < 2 or target_base > 10:
            raise ValueError("Invalid base: %s" % target_base)
        if not is_valid_number(number, source_base):
            raise ValueError("Not a base %s number" % source_base)
        if source_base == target_base:
            return number

    exponent = int(log(number, target_base))
    most_significant_bit = source_base ** exponent
    number -= target_base ** exponent

    return most_significant_bit + convert(
        number,
        source_base,
        target_base,
        validate=False
    )


if __name__ == '__main__':
    print(convert(0x2a, 10, 2))
    print(convert(101010, 2, 10))